calculus problem
glangsing
precalc_problem.docx1. Write the equation below in its equivalent exponential form.
2. Write the first four terms of the sequence whose general term is given below:
an = 4(3n – 1)
3. Use the addition method to solve the system below:
4x + 27y = 27
8x – 3y = -3
4. In the right triangle ABC below, C is the right angle, and two sides are given. Find sin θ of the given angle.
The sin of an angle in a right triangle is equal to the ratio of the opposite side to the hypotenuse.
6. Find the area of a triangle with these measurements: C = 100º, a = 1 yard, and b = 8 yards. Round your answer to the nearest square unit.
7. Solve the right triangle in the figure below in which A = 51.9º and c = 51.2. Round lengths to one decimal place, and express angles to the nearest tenth of a degree.
8. Plot the complex number -3 + 6i.
12. Find the rectangular coordinates of the point whose polar coordinates are (3, -270º)
13. Complete the identity below:
15. If the sequence below is a geometric sequence, find the common ratio.
16. Graph the solution set of the system of inequalities below.
17. Find the maximum and minimum values of the given objective function of a linear programming problem. The figure illustrates the graph of the feasible points.
Objective function: z = 5x + 8y
18. Use Gauss-Jordan elimination to solve the system x – y + 3z = 0, 2x + 2y – z = 9, and –x + 5y – 10z = 4
21. Write an equation for the ellipse with vertices (2, 2), (4, 2), (3, -1) and (3, 5).
23. What is the standard form equation of a parabola with directrixx = -2 and focus (2, 0)?
26. Estimate the following limit using a table:
27. Use properties of limits to compute the following limit exactly.
28. Use the limit definition to compute f’(x) if f(x) = 6x2 – 9.
0,2π[ )
0,2p
[
)
sin−1 −0.5( )
sin
-1
-0.5
()
u i v
uiv
4 3 , 8 3 , 16 3 , 32 3 , 64 3
4
3
,
8
3
,
16
3
,
32
3
,
64
3
y < −x + 8
y<-x+8
y > 8x − 3
y>8x-3
1 2 −8 3 4 0
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
12
-83
40
é
ë
ê
ê
ê
ù
û
ú
ú
ú
6 1 −1 8
⎡
⎣ ⎢
⎤
⎦ ⎥
61
-18
é
ë
ê
ù
û
ú
6 2 −1 0 3 −3 9 −1 7
62-1
03-3
9-17
x − 3( )2 4
− y + 2( )2 1
=1
x-3
()
2
4
-
y+2
()
2
1
=1
x = 1 2 t + 6
x=
1
2
t+6
y = cost −sint
y=cost-sint
r = 1
6+ 4sinθ
r=
1
6+4sinq
lim x→−2
x2 − 4 x + 2
lim
x®-2
x
2
-4
x+2
log5 25 = x
log
5
25=x
lim x→0
x + 7 − 7 x
lim
x®0
x+7-7
x
5π 4
5p
4
cos α − β( )
cosa-b
()
